Alternatively, [1]} propose a top-down pruning methodology based on SC,
which searches for the final model \(\widehat{\Theta }\) 
from a set of candidate change point estimators, say \(\mathcal {C}\) , according to the following rules:
(i) Adding further estimator to \(\widehat{\Theta }\)  monotonically increases SC, and
(ii) among all subsets satisfying (i), \(\widehat{\Theta }\)  attains the minimal cardinality
and (if there exist ties) the minimum SC.
This approach gains computationally
compared to minimising the SC exhaustively among all the \(2^{\vert \mathcal {C} \vert }\)  subsets of \(\mathcal {C}\) ,
and achieves consistency in multiple change point estimation
under general assumptions permitting dependence and heavy-tailedness in \(\lbrace \varepsilon _t\rbrace \) .
A localised version of the pruning method attaining linear complexity is proposed
for further computational consideration,
and it is shown to match the minimax optimal multiscale separation and localisation rates,
when applied to the candidates generated by a multiscale MOSUM procedure.
[2]} explore the top-down approach
under a parametric modelling assumption on \(\lbrace \varepsilon _t\rbrace \) ,
which effectively avoids the difficult task
of evaluating the information criterion at a model under-specifying the number of change points.
